https://doi.org/10.1140/epjst/e2013-02027-6
Regular Article
Dynamics of three Toda oscillators with nonlinear unidirectional coupling
1 Radiotechnical Department, Saratov State Technical University, Polytechnicheskaya 77, Saratov 410054, Russia
2 Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
a e-mail: przemyslaw.perlikowski@p.lodz.pl
Received: 16 July 2013
Revised: 13 August 2013
Published online: 28 October 2013
We study the dynamics of three unidirectionally coupled Toda oscillators with nonlinear coupling function in the form of first three terms of Taylor power series. We analytically investigate how the coupling influence the stability of steady state. Basing on calculation of the first Lyapunov coefficient, we show that destabilization may occur by the sub- or supercritical Andronov-Hopf bifurcation. Born periodic solutions are calculated using path-following as a function of coupling strength and Taylor series coefficients. We present that initially stable or unstable branch of periodic solutions may undergo a sequence of bifurcations including: period doubling, Neimark-Saker and fold.
© EDP Sciences, Springer-Verlag, 2013